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This study introduces an adaptive mesh refinement based on edge-based smoothed finite element method (S-FEM) to solve boundary value problems in two-dimensional gradient elasticity. The noteworthy features of the proposed S-FEM is incorporated in the quadtree decomposition framework. Then this framework is utilised to validate the stress-based Ru-Aifantis theorem of gradient elasticity. Since, the high-order differential equation is split into two second-order differential equations within the theorem, both local displacement and non-local stress fields are computed, respectively.
The non-local stress distribution is used for the quadtree refinement which is considered as polygonal element scheme in S-FEM. The systematic numerical experiments are investigate to determine the efficacy of the internal length scale on stress concentration. The proposed method with the local refinement with fewer degrees of freedom is compared to uniform meshes.

computation, modeling, simulation, numerical methods